The Effects of Rotor Blade Angle on Autorotation and Drag
Graham, Michael
Introduction
Autorotation is when an object with propeller blades, usually a helicopter, experiences rotation when falling[1]. Helicopter pilots use this effect in engine-failure situations by disengaging the rotor, allowing it to spin. As it falls, the drag from the spinning propeller slows the helicopter down so the crash is not as severe[1]. A similar effect can be seen in maple seeds: their small “propeller” allows them to fall gently to the ground instead of falling straight down. The longest helicopter autorotation in history was performed by Jean Boulet in 1972 from 12,440 meters in the air. Due to the -63°F temperature, his engine failed and he was forced to land with nothing more than autorotation[4].
In the following video, this helicopter is landing using autorotation: the engine is not powering the main rotor at all. Although the rotors have some inertia left over from when they were being powered, the main thing causing them to spin is the air moving up and through the propeller.
The slowing down of an object while falling due to air pressure is called drag. The acceleration of an object is given by the equation a = (mg – D)/m where a is the object's acceleration, m is the object's mass, D is the drag, and g is the gravitational constant (approx. 9.8)[2]. As drag increases, acceleration decreases.
What we were wondering for this experiment was how the angle of the propeller blades affected both the autorotation of a falling object and its velocity. The ways in which wing angle affect lift in airplanes have already been examined[3], but we want to see what happens if you have rotating blades that are perfectly flat. We predict that the rotation and drag will peak when the blades are at 45 degrees because it is halfway between the two extremes, (0 and 90) so the drag and the force exerted by the turning propeller would be balanced. This would be similar to how a cannonball fires the farthest if the cannon is at 45 degrees.
Procedure
For our experiment we first got our supplies: some dowels, weights, some string, some paperboard, and some cardboard. Then, after we had what we needed, we took some of the cardboard and cut it into a large circle. We then painted lines on the circle at 45˚ intervals (to allow us to count the rotations). Then we cut our paperboard into 8 x 15 rectangles. We took each wooden dowel and glued a pair of rectangles to it at different angles to one another (0˚, 30˚, 45˚,60˚, and 90˚). Then, we ties a string in the center of each one, with weights at the other end of the string to make its descent as straight as possible.
We used a laptop's built in webcam to record each rig falling. Then, in iMovie, we timed from when the rig dropped to when it hit the ground. We were also able to review the footage in slow-motion so we could record how many rotations the apparatus made before hitting the ground.
After collecting a set of data with the wings in one position, we would change it and run the test again.
Results
The following table shows the time taken for each fall:
Degrees
Test1
Test2
Test3
0˚
0.9
0.9
1
30˚
0.9
0.7
1
45˚
0.9
0.8
0.9
60˚
1
1
0.9
90˚
0.6
0.7
0.6
The following table shows the number of rotations the blades made during the fall:
Degrees
Test1
Test2
Test3
0˚
0
1/8
0
30˚
2
15/8
2
45˚
9/8
9/8
1
60˚
1
7/8
1
90˚
0
1/8
0
We did a curve fit on the blade angle vs. time chart in logger pro. We chose to fit the data to a sine function because, after the blade angle goes past 90 degrees, it doubles back on itself (for example, a blade angle of 30 degrees would yield the same number of rotations as a blade angle of 90+30 degrees). The red lines connect the data points and the black line is the graph of the sine function.
As shown in the picture, the sine function is defined by the equation
y = 0.911*sin(0.067*x + 5.541) + 0.802
Where "y" represents rotations and "x" represents blade angle.
We made another graph of blade angle vs falling time. We did a linear fit, and the slope of the line was extremely close to zero, suggesting that drag is essentially constant, no matter what the blade angle. The equation was
y = -0.0026x + 0.9734
Conclusions
From our results we can conclude that rotation peaks closer to 30 degrees than any other angle. We can also conclude that blade angle has almost no effect on drag. This makes sense now because, since 45 degrees is steeper, it allows more air to simply move past it instead of going to the side and generating rotation. However, we were only able to have 3 data samples for each angle measure, so this test may need to be revisited. Also, the act of letting go of the apparatus can sometimes alter the outcome if done improperly, so a more controlled experiment might have a device to let the propeller go in the exact same way each time. A more firmly positioned camera may help as well: it's hard to keep a camera still with just your hands, so it's more difficult to see whats happening in the video.
Further experiments might include how blade size, blade shape, or weight effect autorotation.
Table of Contents
The Effects of Rotor Blade Angle on Autorotation and Drag
Graham, Michael
Introduction
Autorotation is when an object with propeller blades, usually a helicopter, experiences rotation when falling[1]. Helicopter pilots use this effect in engine-failure situations by disengaging the rotor, allowing it to spin. As it falls, the drag from the spinning propeller slows the helicopter down so the crash is not as severe[1]. A similar effect can be seen in maple seeds: their small “propeller” allows them to fall gently to the ground instead of falling straight down. The longest helicopter autorotation in history was performed by Jean Boulet in 1972 from 12,440 meters in the air. Due to the -63°F temperature, his engine failed and he was forced to land with nothing more than autorotation[4].
In the following video, this helicopter is landing using autorotation: the engine is not powering the main rotor at all. Although the rotors have some inertia left over from when they were being powered, the main thing causing them to spin is the air moving up and through the propeller.
The slowing down of an object while falling due to air pressure is called drag. The acceleration of an object is given by the equation a = (mg – D)/m where a is the object's acceleration, m is the object's mass, D is the drag, and g is the gravitational constant (approx. 9.8)[2]. As drag increases, acceleration decreases.
What we were wondering for this experiment was how the angle of the propeller blades affected both the autorotation of a falling object and its velocity. The ways in which wing angle affect lift in airplanes have already been examined[3], but we want to see what happens if you have rotating blades that are perfectly flat. We predict that the rotation and drag will peak when the blades are at 45 degrees because it is halfway between the two extremes, (0 and 90) so the drag and the force exerted by the turning propeller would be balanced. This would be similar to how a cannonball fires the farthest if the cannon is at 45 degrees.
Procedure
For our experiment we first got our supplies: some dowels, weights, some string, some paperboard, and some cardboard. Then, after we had what we needed, we took some of the cardboard and cut it into a large circle. We then painted lines on the circle at 45˚ intervals (to allow us to count the rotations). Then we cut our paperboard into 8 x 15 rectangles. We took each wooden dowel and glued a pair of rectangles to it at different angles to one another (0˚, 30˚, 45˚,60˚, and 90˚). Then, we ties a string in the center of each one, with weights at the other end of the string to make its descent as straight as possible.
We used a laptop's built in webcam to record each rig falling. Then, in iMovie, we timed from when the rig dropped to when it hit the ground. We were also able to review the footage in slow-motion so we could record how many rotations the apparatus made before hitting the ground.
After collecting a set of data with the wings in one position, we would change it and run the test again.
Results
The following table shows the time taken for each fall:
We did a curve fit on the blade angle vs. time chart in logger pro. We chose to fit the data to a sine function because, after the blade angle goes past 90 degrees, it doubles back on itself (for example, a blade angle of 30 degrees would yield the same number of rotations as a blade angle of 90+30 degrees). The red lines connect the data points and the black line is the graph of the sine function.
As shown in the picture, the sine function is defined by the equation
y = 0.911*sin(0.067*x + 5.541) + 0.802
Where "y" represents rotations and "x" represents blade angle.
We made another graph of blade angle vs falling time. We did a linear fit, and the slope of the line was extremely close to zero, suggesting that drag is essentially constant, no matter what the blade angle. The equation was
y = -0.0026x + 0.9734
Conclusions
From our results we can conclude that rotation peaks closer to 30 degrees than any other angle. We can also conclude that blade angle has almost no effect on drag. This makes sense now because, since 45 degrees is steeper, it allows more air to simply move past it instead of going to the side and generating rotation. However, we were only able to have 3 data samples for each angle measure, so this test may need to be revisited. Also, the act of letting go of the apparatus can sometimes alter the outcome if done improperly, so a more controlled experiment might have a device to let the propeller go in the exact same way each time. A more firmly positioned camera may help as well: it's hard to keep a camera still with just your hands, so it's more difficult to see whats happening in the video.
Further experiments might include how blade size, blade shape, or weight effect autorotation.
References
1. Rasheed, Adam(2010). “A Maple Leaf Falling in Slow Motion”. Retrieved January 19, 2012. Web: http://ge.geglobalresearch.com/blog/a-maple-leaf-falling-in-slow-motion
2. Glenn Research Center. “Forces on a Falling Object (With Air Resistance)”. Retrieved January 19, 2012. Web: http://www.grc.nasa.gov/WWW/K-12/airplane/falling.html
3. Glenn Research Center. “Inclination Effects on Lift”. Retrieved January 19, 2012. Web: http://www.grc.nasa.gov/WWW/K-12/airplane/incline.html
4.
Padfield, R. R. "Learning to Fly Helicopters." Print. 26 Jan. 2012. <http://books.google.com.au/books?id=CSmVLrllpKUC>.